We present the input-normal Riccati parameterization, a generalization of Kabamba’s input-normal form [1], which allows the continuous parameterization of the set of minimal linear systems of a given order that have distinct singular values; the input-normal Riccati form has no requirement that the underlying system be stable. We also present formulas for the use of the input-normal Riccati parameterization for the synthesis of systems via gradient methods.